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In this study the magnetic order of the spin-1/2 XXZ chain systemCs$_2$CoCl$_4$ in a temperature range from 50 mK to 0.5 K and in appliedmagnetic fields up to 3.5 T is investigated by high-resolution measurements ofthe thermal expansion and the specific heat. Applying magnetic fields along aor c suppresses $T_\textrm{N}$ completely at about 2.1 T. In addition, we findan adjacent intermediate phase before the magnetization saturates close to 2.5T. For magnetic fields applied along b, a surprisingly rich phase diagramarises. Two additional transitions are observed at critical fields $\mu_0H_{SF1}\simeq 0.25$ T and $\mu_0 H_{SF2}\simeq 0.7$ T, which we propose toarise from a two-stage spin-flop transition.

Low-temperature ordered phases of the spin-$\frac{1}{2}$ XXZ chain system Cs$_2$CoCl$_4$